Transcription

2 Computers and Electricity A gate is a device that performs a basic operation on electrical signals Gates are combined into circuits to perform more complicated tasks 2

3 Constructing Gates A transistor is a device that acts, depending on the voltage level of an input signal, either as a wire that conducts electricity or as a resistor that blocks the flow of electricity A transistor has no moving parts, yet acts like a switch It is made of a semiconductor material, which is neither a particularly good conductor of electricity, such as copper, nor a particularly good insulator, such as rubber 3

4 Constructing Gates The connections of a transistor A transistor has three terminals A source A base An emitter, typically connected to a ground wire If the electrical signal is grounded, it is allowed to flow through an alternative route to the ground (literally) where it can do no harm 4

5 Computers and Electricity There are three different, but equally powerful, notational methods for describing the behavior of gates and circuits Boolean expressions logic diagrams truth tables 5

6 Computers and Electricity Boolean algebra: expressions in this algebraic notation are an elegant and powerful way to demonstrate the activity of electrical circuits 6

7 Computers and Electricity Logic diagram: a graphical representation of a circuit Each type of gate is represented by a specific graphical symbol Truth table: defines the function of a gate by listing all possible input combinations that the gate could encounter, and the corresponding output 7

8 Gates Let s examine the processing of the following six types of gates NOT AND OR XOR NAND NOR Typically, logic diagrams are black and white, and the gates are distinguished only by their shape 8

9 NOT Gate A NOT gate accepts one input value and produces one output value Various representations of a NOT gate 9

10 NOT Gate By definition, if the input value for a NOT gate is 0, the output value is 1, and if the input value is 1, the output is 0 A NOT gate is sometimes referred to as an inverter because it inverts the input value 10

11 AND Gate An AND gate accepts two input signals If the two input values for an AND gate are both 1, the output is 1; otherwise, the output is 0 Various representations of an AND gate 11

12 OR Gate If the two input values are both 0, the output value is 0; otherwise, the output is 1 Various representations of a OR gate 12

13 XOR Gate XOR, or exclusive OR, gate An XOR gate produces 0 if its two inputs are the same, and a 1 otherwise Note the difference between the XOR gate and the OR gate; they differ only in one input situation When both input signals are 1, the OR gate produces a 1 and the XOR produces a 0 13

14 XOR Gate Various representations of an XOR gate 14

15 NAND and NOR Gates The NAND and NOR gates are essentially the opposite of the AND and OR gates, respectively Various representations of a NAND gate Various representations of a NOR gate

16 Gates with More Inputs Gates can be designed to accept three or more input values A three-input AND gate, for example, produces an output of 1 only if all input values are 1 Various representations of a three-input AND gate 16

17 Constructing Gates It turns out that, because the way a transistor works, the easiest gates to create are the NOT, NAND, and NOR gates. Source is a consistent voltage source. V out = V in ; V out =(V 1 V 2 ) ; V out =(V 1 +V 2 ) Constructing gates using transistors 17

18 Circuits Two general categories In a combinational circuit, the input values explicitly determine the output In a sequential circuit, the output is a function of the input values as well as the existing state of the circuit As with gates, we can describe the operations of entire circuits using three notations Boolean expressions logic diagrams truth tables 18

19 Combinational Circuits Gates are combined into circuits by using the output of one gate as the input for another 19

20 Combinational Circuits Because there are three inputs to this circuit, eight rows are required to describe all possible input combinations This same circuit using Boolean algebra: (AB + AC) 20

21 Now let s go the other way; let s take a Boolean expression and draw Consider the following Boolean expression: A(B + C) Now compare the final result column in this truth table to the truth table for the previous example They are identical 21

24 Adders A circuit called a full adder takes the carry-in value into account A full adder 24

25 Multiplexers Multiplexer is a general circuit that produces a single output signal The output is equal to one of several input signals to the circuit The multiplexer selects which input signal is used as an output signal based on the value represented by a few more input signals, called select signals or select control lines 25

26 Multiplexers A block diagram of a multiplexer with three select control lines The control lines S0, S1, and S2 determine which of eight other input lines (D0 through D7) are routed to the output (F) 26

27 Circuits as Memory Digital circuits can be used to store information These circuits form a sequential circuit, because the output of the circuit is also used as input to the circuit 27

Chapter Goals Chapter 4 Gates and Circuits Identify the basic gates and describe the behavior of each Describe how gates are implemented using transistors Combine basic gates into circuits Describe the

File: chap04, Chapter 04 1. True or False? A voltage level in the range 0 to 2 volts is interpreted as a binary 1. 2. True or False? A gate is a device that accepts a single input signal and produces one

Exclusive OR/Exclusive NOR (XOR/XNOR) XOR and XNOR are useful logic functions. Both have two or more inputs. The truth table for two inputs is shown at right. a XOR b = 1 if and only if (iff) a b. a XNOR

CHAPTER3 QUESTIONS MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) If one input of an AND gate is LOW while the other is a clock signal, the output

Upon completion of unit 1.1, students will be able to 1. Demonstrate safety of the individual, class, and overall environment of the classroom/laboratory, and understand that electricity, even at the nominal

ENGI 24 Experiment 5 Basic Logic Gates OBJECTIVE This experiment will examine the operation of the AND, NAND, OR, and NOR logic gates and compare the expected outputs to the truth tables for these devices.

Chapter 1.10 Logic Gates 1.10 (a) Effects of logic gates AND, OR, NOT on binary signals in a processor Microprocessors are the central hardware that runs computers. There are several components that make

CS61c: Representations of Combinational Logic Circuits J. Wawrzynek October 12, 2007 1 Introduction In the previous lecture we looked at the internal details of registers. We found that every register,

ELG3331: Lab 3 Digital Logic Circuits What does Digital Means? Digital describes any system based on discontinuous data or events. Typically digital is computer data or electronic sampling of an analog

Arithmetic Circuits Addition, Subtraction, & Multiplication The adder is another classic design example which we are obliged look at. Simple decimal arithmetic is something which we rarely give a second

2 Lab 4: Transistors and Digital Circuits I. Before you come to lab... A. Please review the lecture from Thursday, March 6, on Binary Numbers and Manipulations. There were two different handouts containing

OpenStax-CNX module: m46620 1 Secondary Logic Functions: NAND/NOR/XOR/XNOR/Buffer George Self This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 Abstract

Part 2: Operational Amplifiers An operational amplifier is a very high gain amplifier. Op amps can be used in many different ways. Two of the most common uses are a) as comparators b) as amplifiers (either

Design with Multiplexers Consider the following design, taken from the 5 th edition of my textbook. This is a correct implementation of the Carry Out of a Full Adder. In terms of Boolean expressions, this

NOT AND OR XOR NAND NOR Expression 1: It is raining today Expression 2: Today is my birthday X Meaning True False It is raining today It is not raining Binary representation of the above: X Meaning 1 It

Unit 2: Number Systems, Codes and Logic Functions Introduction A digital computer manipulates discrete elements of data and that these elements are represented in the binary forms. Operands used for calculations

Programmable Logic Devices (PLDs) Lesson Objectives: In this lesson you will be introduced to some types of Programmable Logic Devices (PLDs): PROM, PAL, PLA, CPLDs, FPGAs, etc. How to implement digital

Unit: 1 Binary Systems and Logic Circuits 1.1 INTRODUCTION: Electronic systems usually deal with information. Representation of information is called a signal. Signal in electronics is generally in form

WEEK 2.2 CANONICAL FORMS 1 Canonical Sum-of-Products (SOP) Given a truth table, we can ALWAYS write a logic expression for the function by taking the OR of the minterms for which the function is a 1. This

Objectives Having read this workbook you should be able to: recognise the arrangement of NAND gates used to form an S-R flip-flop. describe how such a flip-flop can be SET and RESET. describe the disadvantage

United States Naval Academy Electrical and Computer Engineering Department EC262 Exam 29 September 2. Do a page check now. You should have pages (cover & questions). 2. Read all problems in their entirety.

THE NAND GATE The NAND gate is a popular logic element because it can be used as a universal gate: that is, NAND gates can be used in combination to perform the AND, OR, and inverter operations. The term

1 Digital Logic ircuits 1. Digital Logic ircuits Many scientific, industrial and commercial advances have been made possible by the advent of computers. Digital Logic ircuits form the basis of any digital

Introduction Gates & Boolean lgebra Boolean algebra: named after mathematician George Boole (85 864). 2-valued algebra. digital circuit can have one of 2 values. Signal between and volt =, between 4 and

Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order

Digital Circuits Frequently Asked Questions Module 1: Digital & Analog Signals 1. What is a signal? Signals carry information and are defined as any physical quantity that varies with time, space, or any

6 March 2015 Today we will be abstracting away the physical representation of logical gates so we can more easily represent more complex circuits. Specifically, we use the shapes themselves to represent

Lecture 8: Synchronous Digital Systems The distinguishing feature of a synchronous digital system is that the circuit only changes in response to a system clock. For example, consider the edge triggered

Chapter 4 4.1 The Binary Concept Binary refers to the idea that many things can be thought of as existing in only one of two states. The binary states are 1 and 0 The 1 and 0 can represent: ON or OFF Open

3e4.5 4.201 According to DeMorgan s theorem, the complement of X + Y Z is X Y +Z. Yet both functions are 1 for XYZ = 110. How can both a function and its complement be 1 for the same input combination?

Project Part I 8-bit 4-to-1 Line Multiplexer Specification: This section of the project outlines the design of a 4-to-1 multiplexor which takes two 8-bit buses as inputs and produces a single 8-bit bus

Lecture 14 Let s put together a Manual Processor Hardware Lecture 14 Slide 1 The processor Inside every computer there is at least one processor which can take an instruction, some operands and produce

Combinational Circuits (Part II) Notes This part of combinational circuits consists of the class of circuits based on data transmission and code converters. These circuits are multiplexers, de multiplexers,

Simplifying Logic Circuits with Karnaugh Maps The circuit at the top right is the logic equivalent of the Boolean expression: f = abc + abc + abc Now, as we have seen, this expression can be simplified

BOOLEAN ALGEBRA & LOGIC GATES Logic gates are electronic circuits that can be used to implement the most elementary logic expressions, also known as Boolean expressions. The logic gate is the most basic

Objectives ELEC - EXPERIMENT Basic Digital Logic Circuits The experiments in this laboratory exercise will provide an introduction to digital electronic circuits. You will learn how to use the IDL-00 Bit

EECS 270 Verilog Reference: Combinational Logic 1 Introduction The goal of this document is to teach you about Verilog and show you the aspects of this language you will need in the 270 lab. Verilog is

Problem Session 3 Overview Welcome to Logisim! Logisim is a logic simulator that allows you design and simulate digital circuit using a graphical user interface. It was written by Carl Burch. Logisim comes

Module-3 SEQUENTIAL LOGIC CIRCUITS Till now we studied the logic circuits whose outputs at any instant of time depend only on the input signals present at that time are known as combinational circuits.

Karnaugh Maps Applications of Boolean logic to circuit design The basic Boolean operations are AND, OR and NOT These operations can be combined to form complex expressions, which can also be directly translated

Reading and construction of logic gates A Boolean function is an expression formed with binary variables, a binary variable can take a value of 1 or 0. Boolean function may be represented as an algebraic

CHPTER EIGHT Combinational Logic pplications Thus far, our discussion has focused on the theoretical design issues of computer systems. We have not yet addressed any of the actual hardware you might find